Eratosthenes calculates the Earth's circumference

Duration: 6 minutes and 33 seconds

Country: United States

Language: English

License: CC - Attribution Non-commercial No Derivatives

Genre: Instructional

Views: 1,238 (168 embedded)

Posted by: lolaceituno on Mar 2, 2009

Carl sagan explains how Eratosthenes calculated the circumference of the Earth.

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There was once a time when our little planet seemed immense. When it was the only world we could explore.
Its true size was first worked out in a simple and ingenious way
by a man who lived here in Egypt, in the third century B.C.
This tower may have been a communication star,
part of a network running along the North African coast
by which signal bonfires were used to communicate messages of state.
It also may have been used as a lighthouse,
a navigational beacon for sailing ships out there in the Mediterranean sea.
It is about fifty kilometres west of what was once one of the great cities of the world: Alexandria.
In Alexandria at that time there lived a man named Eratosthenes.
One of his envious contemporaries called him "Beta", the second letter of the Greek alphabet
because, he said, Eratosthenes was second best in the world in everything.
But it seems clear that in many fields, Eratosthenes was "Alfa".
He was an astronomer, historian, geographer, philosopher, poet, theatre critic and mathematician.
He was also the chief librarian of the great library of Alexandria.
And, one day, while reading a papyrus book in the library, he came upon a curious account.
Far to the South, he read, at the frontier outpost of Syene, something notable could be seen on the longest day of the year.
On June 21st, the shadows of a temple column or a vertical stick,
would go shorter as noon approached.
And as the hours crept towards midday, the sun´s rays
would slither down the sides of a deep well
which on other days would remain in shadow.
And then, precisely at noon, columns would cast no shadows
and the sun would shine directly down into the water of the well.
At that moment the sun was exactly overhead.
It was an observation that someone else might easily have ignored.
Sticks, shadows, reflections in wells, the position of the sun...
Simple everyday matters. Of what posssible importance might they be?
But Eratosthenes was a scientist and his contemplation of these homely matters
changed the world, in a way, made the world.
Because Eratosthenes had the presence of mind to experiment
to actually ask whether, back here, near Alexandria, a stick cast a shadow near noon on June the 21st.
And it turns out, sticks do.
An overly skeptical person might have said that the report from Syene was in error.
But it´s an absolutely straightforward observation, and
Why would anyone lie on such trivial matter?
Eratosthenes asked himself how it could be
that at the same moment a stick in Syene would cast no shadow
and a stick in Alexandria, 800 kilometres to the north,
would cast a very definite shadow.
Here´s a map of ancient Egypt.
I've inserted two sticks or obeliscs.
One up here in Alexandria, and one down here in Syene.
Now, if at a certain moment, each stick casts no shadow, no shadow at all,
that´s perfectly easy to understand,
provided the Earth is flat.
If the shadow at Syene has a certain length
and the shadow at Alexandria is the same length,
that also makes sense on a flat Earth.
But, how could it be, Eratosthenes asked,
that at the same instant, there was no shadow at Syene
and a very substantial shadow at Alexandria?
The only answer was that the surface of the earth is curved.
Not only that, but
the greater the curvature, the bigger the difference
in the lengths of the shadows.
The sun is so far away
that its rays are parallel when they reach the Earth.
Sticks at different angles to the sun´s rays
will cast shadows at different lengths
For the observed difference in the shadow lengths
the distance between Alexandria and Syene
had to be about seven degrees along the surface of the Earth.
By that I mean, If you imagine these sticks extending
all the way down to the centre of the Earth,
they would there intersect at an angle of about seven degrees.
Well, 7 degrees is something like 1/50 of the full circumference of the Earth of 360 degrees.
Eratosthenes knew the distance between Alexandria and Syene. He knew it was 100 kilometres.
Why? Because he hired a man to pace out the entire distance
so that he could perform the calculation I'm talking about.
Now, 800 km times 50 is 40,000 km, so that must be the circumference of the Earth.
That´s how far it is to go once around the Earth.
That's the right answer.
Eratosthenes's only tools were sticks, eyes, feet and brains, plus a zest for experiment.
With those tools, he correctly deduced the circumference of the Earth,
to high precision, with an error of only a few percent.
That's pretty good figuring for 2200 years ago.

Eratosthenes calculates the Earth's circumference

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